Magic Square

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 256 megabytes
Time limit: 1.0 seconds

A magic square is a square grid of numbers where the sums of each row, column, and both diagonals are the same.

You will be given a 3x3 magic square of positive integers. However, the magic square is incomplete – there are $N$ missing elements, denoted by the value $0$ .

Solve the magic square.

Input

There will be three lines, each containing three space-separated integers, representing elements of the incomplete magic square.

Exactly $N$ of the elements will be $0$ , indicating a missing value that must be found. All remaining elements will be between $1$ and $10\,000$ (inclusive).

Output

You should print three lines, each containing three space-separated integers, representing elements of the completed magic square.

It is guaranteed that there is a unique solution, and that all elements of the solution will be between $1$ and $10\,000$ (inclusive).

Subtasks

Subtask 1 (25%): $N = 1$
Subtask 2 (25%): $1 \le N \le 2$
Subtask 3 (25%): $1 \le N \le 3$
Subtask 4 (25%): $1 \le N \le 5$

Sample Input 1
```
3 3 6
7 0 1
2 5 5
```
Sample Output 1
```
3 3 6
7 4 1
2 5 5
```
Sample Input 2
```
6 1 0
7 0 3
0 9 4
```
Sample Output 2
```
6 1 8
7 5 3
2 9 4
```

Magic Square

Input

Output

Subtasks

Sample Input 1

Sample Output 1

Sample Input 2

Sample Output 2